The purpose of this study is to assess the durability of response in patients who have been treated with lamivudine and have seroconverted. This definition will be based on laboratory values. Should a patient develop active hepatitis B infection, this study will also provide lamivudine treatment. Early studies have shown that lamivudine has the potential to reduce the levels of hepatitis B DNA in the blood. This may correlate to a positive effect on the liver disease and outcome in seriously ill patients.